Is the length of rectangular field F greater than the length of rectan

In this case, individually, we are able to fairly quickly discern that just the area of F being greater (statement (1)) - or just the width of F being less (statement (2)) cannot be enough information, as we can both answer the question "yes" and "no" within those parameters. So, we'll want to think about whether both statements together are sufficient or neither is sufficient.

When we take the statements together, in order to have a larger area, the (length)*(width) will need to be larger.

So, if we know we have a smaller width - we can conceptually conclude that the length of rectangular field F will need to be greater than the length of rectangular field G

(smaller length)*(larger width) must be true in order to be > (larger length)*(smaller width)

Basically, the length must be larger to outweigh the smaller width and create a greater outcome for (length)*(width).

So, since the length of F must be greater in order for the statements combined to hold true - together, the statements are sufficient! (C)

Since the overlap of the two statements creates a situation such that the length must be larger, we are able to conclude sufficiency. David makes a great point above in that this would not be the case if we were told that the width of F was greater, this would not be enough information - even together - as we could still answer the question "yes" and answer it "no."

It is specifically because we have the must be true parameter around the length being greater that we are able to conclude sufficiency. We know the answer must be "yes."

Hope this helps!

Solution

Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given:

• Two rectangular fields: F and G.

We need to determine:

• Whether the length of rectangular field F is greater than rectangular field G or not.

Let us assume that

• length of field F = Lf and width = Wf
• Similarly, length of field G = Lg and width= Wg

So, to answer this question, we need the length of both the rectangular fields or a relation between them.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1
“The area of F is greater than the area of G.”

• Area of field F = Lf × Wf
• Area of field G = Lg × Wg

Area of field F > Area of field G

• Hence, Lf × Wf > Lg × Wg

However, this does neither give us the value of Lf and Lg nor any relation between them.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2
“The width of F is less than the width of G.”

• Wf < Wg
• From this statement, we cannot find the relation between Lf¬ and Lg.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
From Statement 1:

• Lf × Wf > Lg × Wg ---------(1)

From Statement 2:

• Wf < Wg -----------(2)

If we multiply Lg in the above inequality, we get: Lg × Wf < Lg × Wg ---------(3)

From (1) and (3) inequality, we get:

• Lf × Wf > Lg × Wg > Lg × Wf
• Lf × Wf > Lg × Wf

o Since Wf is positive, we can divide it on both the sides of the inequality and sign will not change.

 Thus, Lf > Lg

Hence, we can find the answer by combining both the statements together.

Thus, the correct answer choice is option C.

(1) Length can be greater or smaller, For example

Area of the rectangle = Length x Width

Area of F=12*10=120; Area of G=10*8=80, but

Area of F=12*10=120; Area of G=13*8=104

Yes or No; Insufficient.

(2) No information about length; Insufficient.

Considering Both:
Area of F=12*10=120; Area of G=10*8=80

Area of F=12*10=120; Area of G=15*8=120; Contradictory with the statements

So, Both statements together give a certain answer.

The answer is C.

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